Study of the one-dimensional Holstein model with next-nearest-neighbor hopping

We present the effect of next-nearest-neighbor hopping on Holstein polarons. The energy and wavefunction of the ground state and first excited state are obtained by using a conjugate-gradient technique on the variational Hilbert space of the electron-phonon (e-ph) system. We increase the size of the variational space systematically to obtain high accuracy. With the converged wavefunction at our disposal we obtain various physical quantities and correlation functions to get a holistic insight into the physics of e-ph interaction. Our study reveals that the effect of next-nearest-neighbor hopping is most prominent at the physically interesting crossover regime of the e-ph coupling and in the adiabatic regime. We have also performed analytical strong coupling second order perturbation with a Lang-Firsov (LF) phonon basis to account for some features in the strong coupling regime.